Consider an experiment with 2 treatments, say Placebo and New Cholesterol Loweri

Question

Consider an experiment with 2 treatments, say Placebo and New Cholesterol Lowering Drug.   Suppose the cholesterol levels for 8 subjects were recorded as follows (H = High, L = Low):

Placebo     HHHL

Drug           LLHL

If there is no difference between the placebo and the drug, these 8 observations can be treated as a random assignment to the two treatments.

Based on the original data, what is the standard deviation of the approximate reference distribution of the test statistic T if there is no difference between the drug and the placebo?

Explanation / Answer

here n1=4, n2=4

we use difference of two treatment (placebo and drung) means using t-test as sample size is less than 30.

The standard deviation of for difference of two treatment means will be sp= square root of the quantity

(n1-1)s12 + (n2-1)s22)/(n1+n2-2)

where s12 is the standard deviation of treatment 1(say placebo) and

s22 is the standard deviation of treatment 2 (say drug)

and t-statistic will be t=(mean1-mean2)/(sp/sqrt(n1+n2-2)) with (n1+n2-2) df

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